New Forest boss Aitor Karanka is willing to let Ward move on as he looks to trim his squad to bring in new signings.
Forest are looking to make several new signings on deadline day and Ward could be one of a number of players to make way at the City Ground.
Ward has found himself on the fringes of the Forest team this season, making only seven appearances off the bench in the current campaign.
Ward, who has 18 months to run on his deal at Forest, is happy to move on in search of regular first-team football in the second half of the season.
A number of clubs have expressed an interest in Northern Ireland international Ward, but Millwall are in pole position to land the 31-year-old.
Millwall have been busy in the transfer market this month and are hoping to tie up a double deal for both Ward and Wolverhampton Wanderers winger Ben Marshall before the transfer window closes at 11:00pm on Wednesday.